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432 Corporate Finance BRILLIANT’S

A firm is evaluating a proposal costing EH$ \$_© EH$ ànmoOb na {dMma H$a ahr h¡ {OgH$s
` 2,00,000. The life of the project is 6 years. The H$m°pñQ>¨J ` 2,00,000 h¡Ÿ& àmoOoŠQ> H$m OrdZ H$mb 6 df©
annual cash inflows are ` 50,000 and there is h¡Ÿ& dm{f©H$ H¡$e BZâbmoO ` 50,000 h¡ d gm°ëdoO d¡ë`y
no salvage value. The IRR of the proposal may
be calculated as follows: Hw$N> ^r Zht h¡Ÿ& ànmoOb Ho$ IRR H$s JUZm Bg àH$ma hmoJr…
Step 1: Make an approximation of the IRR ñQ>on 1: H¡$e âbmo S>mQ>m Ho$ AmYma na IRR H$m
on the basis of cash flow data. A rough AZw_mZ cJmE§Ÿ& no-~¡H$ nr[a`S> Ho$ AmYma na EH$ a\$
approximation may be made with reference to
the pay back period. The pay back period in AZw_mZ cJm`m Om gH$Vm h¡Ÿ&ŸXr JB© pñW{V _| no-~¡H$
the given case is 4 years (2,00,000 ÷ 50,000). nr[a`S> 4 df© (2,00,000 ÷ 50,000) h¡Ÿ&
Step 2: Search for a value nearest to 4 in ñQ>on 2: àoOoÝQ> d¡ë`y EÝ`yQ>r \¡$ŠQ>a (PVAF) Q>o~b
th
the 6 year row of the Present Value Annuity _| 6 df© H$s amo _| 4 H$s d¡ë`y XoI|Ÿ& g~go {ZH$Q>V_
th
Factor (PVAF) table. The nearest figures are d¡ë`y (4.111) 12% aoQ> na VWm (3.998) 13% aoQ> na
given in rate 12% (4.111) and the rate 13%
`h Xem©Vm h¡ {H$ ànmoOb H$m IRR 12% go 13% Ho$
(3.998). It shows that the IRR of the proposal is
expected to lie between 12% and 13%. _Ü` h¡Ÿ&
Step 3: In order to calculate the accurate ñQ>on 3: ewÕ IRR H$s JUZm Ho$ {b`o XmoZm| Xam| Ho$
IRR, find out the NPV of the project for both AmYma na àmoOoŠQ> H$m NPV kmV H$a|:
the rates:
At 12% NPV = (` 50,000 × PVAF 12%, 6 yrs.) – ` 2,00,000
= (` 50,000 × 4.111) – ` 2,00,000 = ` 5,550
At 13% NPV = (` 50,000 × PVAF 13%, 6 yrs) – ` 2,00,000
= (` 50,000 × 3.998) – ` 2,00,000 = ` (–) 100
Step 4: The exact IRR can be calculated by ñQ>on 4: ghr IRR H$s JUZm B§Q>anmoboeZ Ho$ Ûmam H$s
interpolation. As we calculated above, the NPV Om gH$Vr h¡Ÿ& Cnamoº$ JUZm go ñnï> h¡ {H$ 12% Xa na
at 12% is ` 5,550 and at 13%, it is ` (–) 100. NPV ` 5,550 h¡ d 13% na `h ` (–)100Ÿ& AV: dh
Therefore, the rate at which the NPV is zero
will be higher than 12% but less than 13%. By Xa {Og na NPV eyÝ` h¡, 12% go A{YH$ na§Vw 13% go
interpolation technique we can calculate the H$_ hmoJrŸ& BÝQ>anmoboeZ {d{Y go h_ dh Xa kmV H$a gH$Vo
rate at which NPV is zero. It is as follows: h¢ {Og na NPV Oramo hmo OmEŸ& `h Bg àH$ma h¡…

A
IRR = L + (H-L)
A-B 
Where, L = lower discount rate at which NPV is positive.
H = higher discount rate at which NPV is negative.
A = NPV at lower discount rate.
B = NPV at higher discount rate.
5, 550

Thus, IRR = 12% + (13 12) = 12.98%
5, 550 ( 100) 